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A196737 Decimal expansion of (4*Pi^2)/sqrt(35) = A212002/A010490. 0
6, 6, 7, 3, 0, 7, 0, 5, 2, 1, 6, 5, 4, 3, 7, 1, 2, 7, 2, 3, 9, 6, 0, 1, 6, 3, 9, 1, 3, 8, 8, 4, 1, 9, 9, 2, 4, 3, 7, 1, 6, 6, 8, 3, 0, 0, 6, 9, 1, 8, 5, 7, 2, 6, 4, 5, 7, 9, 2, 5, 6, 5, 1, 6, 5, 9, 0, 5, 4, 1, 2, 9, 2, 0, 2, 2, 8, 0, 2, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is exactly equal to (Pi*h)/Spin(5/2), where h = Planck's Constant = A003676 and Spin(n/2) = h/(4*Pi) * sqrt(n(n+2)) = A003676/(10*A019694)) * sqrt(A005563(n)).

Observation: Where G is the universal gravitational constant = A070058 (= 6.67384(80)*10^-11 m^3*kg^-1*s^-2), GM is the standard gravitational parameter, and M'_pbh is one estimate of the mass of a primordial black hole with evaporation time equal to the age of the universe (~ 10^11 kg; see link by Andrew Hamilton below), then this sequence approximates G*M'_pbh*(4*Pi^2)/GM = G*M'_pbh*seconds^2/meter^3. Were this formula to be exact, then, based on the CODATA 2010 value for G, the mass of such a primordial black hole, rounded to 6 decimal places, would be equal to 0.999885*10^11 kg, a figure subject to change based on future empirical measurements of G. Coincidentally, 99.9885(70)% is the estimated relative abundance of the hydrogen-1 isotope (aka "protium") here on planet Earth.

Alternatively, from the formula for a pendulum, T = 2*Pi*sqrt(L/g), where L = Length, T = period and g is acceleration due to gravity, it follows that this sequence is exactly equal to (g*T^2*(h-bar/2))/(L*Spin(5/2)); h-bar/2 = h/(4*Pi) = A003676/(10*A019694) ~ A003676*A081821*A003671*A005600. - Raphie Frank, Jan 04 2013

LINKS

Table of n, a(n) for n=1..81.

B. J. Carr, Primordial black holes: do they exist and are they useful?, Queen Mary University of London.

Andrew Hamilton, Hawking Radiation, University of Colorado at Boulder.

Wikipedia, Gravitational constant

Wikipedia, Isotopes of hydrogen

Wikipedia, Pendulum

Wikipedia, Planck constant

Wikipedia, Spin (physics)

EXAMPLE

6.673070521654371272396016391388419924371668300691857264579256516590541...

CROSSREFS

Cf. A212002, A010490.

Sequence in context: A241057 A247253 A244293 * A070058 A160057 A190145

Adjacent sequences:  A196734 A196735 A196736 * A196738 A196739 A196740

KEYWORD

nonn,cons

AUTHOR

Raphie Frank, Dec 21 2012

STATUS

approved

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Last modified June 5 01:27 EDT 2020. Contains 334828 sequences. (Running on oeis4.)